In the related art, there has been an attempt to control the traveling of an individual vehicle to improve a traffic flow on a road, thereby reducing traffic congestion. For example, Patent Literature 1 describes a preceding vehicle follow-up device which detects a change in the gradient of a traveling road ahead, and if a change in the gradient of the traveling road ahead is detected near a sag (a change point on a road from downhill to uphill) or the like, and performs switching from inter-vehicle distance control to vehicle speed control. In the preceding vehicle follow-up device of Patent Literature 1, the inter-vehicle distance control is switched to the vehicle speed control near the sag, thereby suppressing a variation in the vehicle speed during preceding vehicle follow-up control. In particular, the preceding vehicle follow-up device of Patent Literature 1 prevents a phenomenon in which a variation in the vehicle speed of the preceding vehicle is amplified and propagated to a succeeding vehicle.